Marketing of products entails balancing the valuations placed on items by a buyer against the prices (or, more generally, contracts) set by the seller. In general, if the buyer's valuation of an item is greater than the price of the item, then the sale is likely to occur; conversely, if the buyer's valuation is less than the price of the item then no sale is likely.
More quantitatively, a “buyer's surplus” from a purchase can be identified as the difference between the buyer's valuation of the item and the sale price. A “seller's profit” is determined by the sale price minus the cost to the seller in obtaining and marketing the item. The seller would like to sell the item at the highest price possible, since this maximizes the seller's revenue; however, if the price is set too high, and more particularly above the buyer's valuation, then no sale will occur and no revenue is obtained. Further complicating the situation is that in the case of multiple buyers, different buyers may place different values on the item, or an individual buyer may have different valuations at different times.
In existing approaches, the seller sets the price for an item based on the seller's past experience or other available information, and then adjusts the price upward or downward over time based on sales. For example, if an unexpectedly low number of sales is achieved at the initial price, the seller may lower the price in order to encourage additional sales. Conversely, if sales are brisk at the initial price then the seller may try increasing the price. If sales volume is maintained (or decreases only slightly) at the higher price, then the seller's revenue is increased. These approaches are sometimes referred to as censored price experiment (CPE) approaches. The seller estimates the distribution of buyers' valuations from censored observations (that is, observations that the valuation is greater than the price or that the valuation is less than the price; more generally a censored observation is one that is only known to come from some set).
Other approaches have been attempted for price optimization. These approaches typically are variants of the price adjustment scheme, sometimes under different nomenclature. For example, in the automotive industry it is known to offer price rebates to encourage purchases. Such rebates are simply short-term price adjustments, and can be used to learn customer valuations of the automobiles.
Other approaches attempt to rely upon self-reporting by buyers. An extreme example of this is the “pay what you like” restaurant model. In this model, the buyer actually sets the price by being allowed to pay whatever the buyer believes the restaurant meal was worth. See, e.g. “Pay-what-you-like restaurants”, http://www.cnn.com/2008/TRAVEL/04/01/flex.payment/index.html (last accessed May 7, 2010).
The various learning models are susceptible to various errors. For example, at certain times American car buyers have come to expect certain automobile manufacturers to offer frequent rebates, and delay purchase until the next rebate offer. The “pay what you like” approach is reliant upon honesty of the self-reporting, and in this regard introduces a problematic self-interest factor into the self-reporting, in that it is in the restaurant patron's self-interest to pay less than the patron actually believes the meal was worth and thereby save money.
More generally, any valuation approach that is based on collecting data from buyers (or, more generally, offerees—in procurement, for example, the offeror may be the buyer and the offeree may be the seller, that is, the potential supplier) is susceptible to error due to large deviations in valuations derived from buyer responses to an offer. Large deviations may result from intentional “lies” by buyers, or may result from inadvertent overvaluation or undervaluation. An example of the latter is an uninformed buyer who grossly overpays for an item out of ignorance.